Topic

 

Linear Algebra

Linear algebra is the branch of mathematics concerning linear equations, linear maps, and their representations in vector spaces and through matrices.

Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as basically the application of linear algebra to spaces of functions.

Linear algebra is also used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point.

from Linear Algebra - Wikipedia

This topic includes the following resources and journeys:

 

 

Linear Algebra Review

J. Zico Kolter
Intermediate
Course
Theory

This short course is a quick review of linear algebra, intended for students who have already taken a previous course in linear algebra or have some experience with vectors and matrices. The...

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Gaussian/Normal Distributions

Christopher Lum
99 min
Beginner
Video
Theory

In this video we discuss the Gaussian (AKA Normal) probability distribution function. We show how it relates to the error function (erf) and discuss how to ...

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Inner Products in Hilbert Space

Steve Brunton
8 min
Intermediate
Video
Theory

This video will show how the inner product of functions in Hilbert space is related to the standard inner product of vectors of data.

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Unitary Transformations

Steve Brunton
12 min
Beginner
Video
Theory

This video discusses unitary matrix transformations and how they relate to the geometry of the singular value decomposition (SVD).

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crash course on complex numbers

Iman Moazzen
10 min
Beginner
Video
Theory

In this video, we quickly review “Complex Numbers”. The following materials are covered:1- Cartesian and polar representation of complex numbers2- how to con...

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